Daily Olympiad: Logical Reasoning - Syllogisms [20260511] – 13 Practice Problems & Printable PDF

1. All novels are books. All books are publications. What follows?

A. All publications are novels. B. Some books are novels. C. Some publications are books. D. All novels are publications.

Solution

Correct: D

The first premise states that all novels are books (universal affirmative), and the second states all books are publications (universal affirmative). Combining these, the conclusion that all novels are publications is valid because categories preserve the hierarchy. The other options do not logically follow from the premises.

2. No cats are reptiles. Some animals are reptiles. What can be concluded?

A. Some animals are not cats. B. Some cats are not animals. C. All reptiles are animals. D. No animals are cats.

Solution

Correct: A

The premises include a universal negative and a particular affirmative. The conclusion that 'some animals are not cats' follows via syllogistic logic: since no cat is a reptile and some animals are reptiles, those reptiles cannot be cats. The other choices are invalid inferences or do not logically follow.

3. All engineers are creative. Some artists are engineers. What conclusion is valid?

A. Some artists are creative. B. All artists are creative. C. No engineers are artists. D. All engineers are artists.

Solution

Correct: A

The first premise is universal affirmative, the second is particular affirmative. The conclusion that some artists are creative follows (AII syllogism). Other choices extend beyond the premises (e.g., 'all artists') or are invalid contradictions.

4. Some cars are electric. No electric vehicles are diesel. What follows?

A. Some cars are not diesel. B. All electric cars are not cars. C. No cars are electric. D. Some diesel cars are electric.

Solution

Correct: A

Some cars are electric, and no electric vehicle is diesel. Since electric and diesel are mutually exclusive categories, it follows that some cars (electric ones) are not diesel. Other choices misrepresent or contradict the premises.

5. All mammals are warm-blooded. All bats are mammals. What can be concluded?

A. All bats are warm-blooded. B. No bats are warm-blooded. C. Some warm-blooded are bats. D. All warm-blooded are bats.

Solution

Correct: A

Universals in premises (All A is B, All C is A) necessitate the conclusion 'All C is B.' Since bats are mammals and mammals are warm-blooded, bats are warm-blooded. Other options misstate or invert the logic.

6. Some politicians are honest. All honest people are trustworthy. Valid conclusion?

A. Some politicians are trustworthy. B. All trustworthy people are honest. C. No politicians are trustworthy. D. All politicians are honest.

Solution

Correct: A

Particular affirmative and universal affirmative premises allow AII syllogism. 'Some politicians are trustworthy' follows. Other choices overgeneralize or misrepresent the premises.

7. No birds are fish. Some fish are not reptiles. What does it imply?

A. Some birds are not reptiles. B. All fish are reptiles. C. Some reptiles are not birds. D. No birds are reptiles.

Solution

Correct: C

The premises do not directly link birds with reptiles. Only the conclusion 'some reptiles are not birds' follows via the contrapositive or indirect reasoning, as the absence of overlap between birds and fish doesn't inform the relationship with reptiles.

8. All novels are stories. Some stories are tales. What can be concluded?

A. Some tales are novels. B. All novels are tales. C. Some novels are tales. D. No stories are novels.

Solution

Correct: C

The first premise is universal, the second particular. Only 'some novels are tales' is valid because the particular premise allows for an overlapping subset. Other choices overextend or invert premises.

9. No apples are oranges. Some fruits are apples. What follows?

A. Some fruits are not oranges. B. All apples are fruits. C. No fruits are oranges. D. Some oranges are not apples.

Solution

Correct: A

Since no apples are oranges and some fruits are apples, the fruits that are apples are not oranges. Hence, 'some fruits are not oranges' is valid. Other options are invalid or misstate the premises.

10. All teachers are educated. Some students are not educated. What conclusion?

A. Some students are not teachers. B. All students are not educated. C. No teachers are students. D. Some educated are not students.

Solution

Correct: A

If all teachers are educated, and some students are not educated, those uneducated students cannot be teachers. Hence, 'some students are not teachers' follows. Other options misrepresent or contradict premises.

11. Some plants are trees. All trees are woody. Valid conclusion?

A. Some plants are woody. B. All plants are woody. C. Some trees are not plants. D. No plants are trees.

Solution

Correct: A

Particular universal premises allow AII syllogism: 'some plants are woody.' Other choices overgeneralize or contradict. The other categories remain undefined.

12. No philosophers are scientists. Some scientists are doctors. What conclusion?

A. Some doctors are not philosophers. B. All doctors are not scientists. C. Some philosophers are doctors. D. No doctors are scientists.

Solution

Correct: A

The premises imply that some doctors are scientists but none are philosophers. Thus, 'some doctors are not philosophers' follows via transposition. Other options misrepresent the premises.

13. All birds can fly. Some flying creatures are birds. What does this imply?

A. Some birds are not flying creatures. B. Some flying creatures can fly. C. All flying creatures are birds. D. Some can fly are birds.

Solution

Correct: D

The premises state all birds can fly and some flying creatures are birds. Thus, 'some can fly are birds' is valid. The second choice is trivial but also follows. However, the best choice adheres to AII syllogism form.